I like these questions! They make me think.
Being in human form definitely dampens the god's powers. Imagine being wrapped up head to toe in duct tape. All your senses, from touching to seeing to even smelling, are all blunted. Being in human form is the god's equivalent of being partially blind, deaf, and mentally handicapped. Some of the gods are going nuts from the sensory deprivation...
As for the hosts, think of the gods as water. They have a spirit form [steam], an "elemental" form [water]*, and a physical form [ice]. The magical bindings are essentially an ice box that traps the water and forces it to stay as ice. The mage's job is to keep the box tightly sealed, make sure there are no holes it could leak through, and when a noble demands the god's power, to open the box juuuuuuuuuuust enough to let the god work its magic.
The reason I don't want to give them a human host is that
1] They already embattled in a power struggle with the nobles and the mages. A third party might be overkill.
2] Recall that the original god was tortured to give up the Names of his colleagues. If the body was a human host, he probably could have just let the host die and his spirit be released. But he couldn't. Which implies that his body cannot die. Which means that the body itself was immortal. Which sucks for the gods, because they can be tortured again and again for centuries, without the relief of death.
3] The mages who captured the god originally did it by accidentally. It's not like they said, "Let's trap him in this plane of existence and abuse the hell out of him!" More like they thought, "Hmmm, we now have the god's Name. Let's do something cool with it!" They wouldn't have had a body for him to inhabit; they just bound him to the body he already showed up in.
Now I just need a name for the RP, and I'll get OOC Discussion thread up and running. Everyone can go claim their gods and nobles there. [I gots dips on the god of love

]
*A god of water's elemental form would be water, obviously. A god of beauty's elemental form might be a stroke of inspiration, a god of love's form might be the fleeting feeling of butterflies in the stomach.EDIT:
A few words of magic.
Magic is a language. Spells are essentially poems in the divine word of godspeech. While an apprentice can shout out the word for fire to ignite a small flame, true magic is weaving the words into a lyrical phrase, a form both elegant and efficient. It can also be written, hand-signed, and if the apprentive has a creative streak, painted, sculpted, or even danced!
Like music, anyone can be taught godspeech, but its easier to do it while young, and some people are naturally gifted at it. Commoners know only a few words and use them clumsy at best. However, there are talismans and enchantments they can purchase from the local songcaster that are imbued with magic, if they need it.
Magic cannot influence a sentient being. One cannot take over another's mind or force him to act against his will. One can only do that if they know the creature's True Name, or in a god's case, simply overwhelm its will with the
magnitude of its power.
One little known fact about mages is that they are as bound to service to the noble as the god. The mage is the leash the noble weilds to keep the god in line. When a god is perchased, the mage signs a contract in godspeech that ultimately states that he is legally and magically obligated to heed the words of the owner. He then signs with his True Name. If a god had been given to a noble without a mage to buffer him, the noble, with no magical training to fortify him, would be inundated by the god's power.
The mage and god share an intimate connection. While not telepathic, the duo are constantly embroiled in a mental and emotional tug of war. Mages are trained to brace their minds against the god's intrsion, but it can take an exhausting toll. It is not uncommon for a mage, after years of enduring mental assault, to request a different assignment from his magister.